On a sequence conjectured to have ideal 2-level autocorrelation function
Anchung Chang, P. Gaal, Solomon W. Golomb, Guang Gong, P. Vijay Kumar · 2002
No, Golomb, Gong, Lee and Gaal conjectured that a certain family of sequences having a convenient trace description possesses the ideal autocorrelation property. Numerical results obtained by the authors of the present paper indicate that the linear cyclic code generated by the terms of the ideal autocorrelation sequence has the same 5-level weight distribution as does the dual of the triple-error correcting primitive BCH code. It is shown that the conjectured autocorrelation sequences are balanced. It is proven that the dual of the cyclic code generated by the sequences has a minimal distance of at least 7. Also, a divisibility result is given concerning the weights of the cyclic code.